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Sufficient Fritz John Type Optimality Criteria and Duality for Control Problems
Department of Mathematics, Jaypee University of Engineering and Technology, Guna, India
- 1 Department of Mathematics, Jaypee University of Engineering and Technology, Guna, India
- 2
American Journal of Industrial and Business Management·Volume 03 (2013)·Pages 237–244·Published 15 April 2013·DOI10.4236/ajibm.2013.32029
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Abstract
Sufficient Fritz John optimality conditions are obtained for a control problem in which objective functional is pseudoconvex and constraint functions are quasiconvex or semi-strictly quasiconvex. A dual to the control problem is formulated using Fritz John type optimality criteria instead of Karush-Kuhn - Tucker optimality criteria and hence does not require a regularity condition. Various duality results amongst the control problem and its proposed dual are validated under suitable generalized convexity requirements. The relationship of our duality results to those of a nonlinear programming problem is also briefly outlined.
KeywordsSufficient Optimality CriteriaControl ProblemFritz John Type DualNonlinear Programming ProblemGeneralized Convexity
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